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This paper presents a decentralized model predictive control approach for the coordination of autonomous vehicles at intersections. A linear quadratic optimal controller is introduced for each vehicle with predefined path, in order to minimize energy as well as to pass intersection smoothly. We guarantee collision avoidance by adding linear constraints to the optimization problem. We apply the so-called soft constraints for the collision avoidance problem to reduce the computation time in order to be able to run the simulations in real-time. In addition, the method can take into account crossing of vehicles in platoons by extending the linear quadratic cost functions.